Approximate Projected Consensus for Convex Intersection Computation: Convergence Analysis and Critical Error Angle
2014 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 7, 1722-1736 p.Article in journal (Refereed) Published
In this paper, we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets, where each set corresponds to one network node. Instead of assuming exact convex projection that each node can compute, we allow each node to compute an approximate projection with respect to its own set. After receiving the approximate projection information, nodes update their states by weighted averaging with the neighbors over a directed and time-varying communication graph. The approximate projections are related to projection angle errors, which introduces state-dependent disturbance in the iterative algorithm. Projection accuracy conditions are presented for the considered algorithm to converge. The results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected. In addition, we show that pi/4 is a critical angle for the error of the projection approximation to ensure the boundedness. Finally, the results are illustrated by simulations.
Place, publisher, year, edition, pages
2014. Vol. 59, no 7, 1722-1736 p.
Approximate projection, intersection computation, multi-agent systems, optimal consensus
IdentifiersURN: urn:nbn:se:kth:diva-148356DOI: 10.1109/TAC.2014.2309261ISI: 000338353300003ScopusID: 2-s2.0-84903287276OAI: oai:DiVA.org:kth-148356DiVA: diva2:736523
FunderKnut and Alice Wallenberg FoundationSwedish Research Council
QC 201408072014-08-072014-08-052014-08-07Bibliographically approved